Which Math Books Are Best for Differential Calculus and Polar Coordinates?

[Saitama]

The college I am currently in has started with Differential Calculus. Due to some reasons I haven't been able to attend the lectures. The current book assigned to us is of no help. The book only shows the solved problems on the topic with very less introduction and no geometrical meaning. I don't know to which area of mathematics the following topics belong and thus I am unable to search for any book.

The following are already covered in the lectures:
Asymptotes
Curvature
Curve Tracing
Partial Differentiation
Maxima and minima of functions with two variables
Jacobians
Envelopes

The above topics were under the section "Differential Calculus" in the book I am assigned. In the next semester, I guess the instructor will begin with Integral Calculus. It would be great if anyone could suggest some books. Also, I heard my instructor talking about Polar coordinates. Please suggest a book for that too.

Thanks!

 

[verty]

The college I am currently in has started with Differential Calculus. Due to some reasons I haven't been able to attend the lectures. The current book assigned to us is of no help. The book only shows the solved problems on the topic with very less introduction and no geometrical meaning. I don't know to which area of mathematics the following topics belong and thus I am unable to search for any book.

The following are already covered in the lectures:
Asymptotes
Curvature
Curve Tracing
Partial Differentiation
Maxima and minima of functions with two variables
Jacobians
Envelopes

The above topics were under the section "Differential Calculus" in the book I am assigned. In the next semester, I guess the instructor will begin with Integral Calculus. It would be great if anyone could suggest some books. Also, I heard my instructor talking about Polar coordinates. Please suggest a book for that too.

Thanks!

You've got a mix of topics from one variable and multivariable calculus which is going to make it difficult to find the right book. Also I know that you like tough problems. So, I recommend these two instead:

Problems in Calculus of One Variable - Maron
http://archive.org/details/CalculusOfSeveralVariables

Both are older books from the 70's although Maron is in print in India, you can find it on ebay.in for example, but the second I could only find shipping from the UK or the USA, I don't know where you could find a paper version of it.

Another option is to get the book Calculus, One and Several Variables - Salas, Etgen, Hille, you'll find it on ebay.in too.

If you need better explanations for some things, look at MIT's stuff here and here, or the other versions they have, plus videos of course.

I should mention that the Marder book may need you to know the one variable material but it definitely looks great to work though. In particular, it has Jacobians and envelopes listed in the contents.

 

[Saitama]

You've got a mix of topics from one variable and multivariable calculus which is going to make it difficult to find the right book. Also I know that you like tough problems.

This time, I am not in search of any challenging problems in Engineering Calculus. I can't give much time to college studies at the moment, because of the same reasons that I could not attend the lectures. Its difficult to explain my current situation. Its not that I am trying to run away from studies, but the problem is, I have other subjects and topics to take care of.

I should have checked the syllabus before making my post. The first semester syllabus also include the Integral Calculus. I will copy-paste the syllabus of both the semesters.

Semester I:

Section A​

Differential Calculus: Partial differential and its applications, Maxima and Minima of two and more independent variables, Jacobians, Asymptotes, Curvatures (formulae without proofs), Envelopes and Curve tracing.

Section B​

Integral Calculus: Gamma and Beta functions, Rectification, Volume and surface of solids of revolution. Differentiation under the integral sign. Double and triple integrals with their applications to area, volume, surface area and mass. Centre of gravity and moment of inertia.

Semester II:

Section A​

Ordinary Differential Equations: Differential equations of the first order and first degree, Differential equations of the first order but not of the first degree. Linear differential equations with constant coefficients, Linear homogeneous differential equations. Linear Differential Equations of second order including method of variation of parameters. Solid Geometry: Sphere-Equation in different forms, section by a plane, sphere through a given circle.Intersection of a sphere and a line, and of two spheres, tangent plane, Orthogonal sphere. (Cartesian form) Cone and Cylinder-Equations and their properties (Cartesian from).

Section B​

Mechanics: Equilibrium of a rigid body under the action of three coplanar forces. Friction (excluding braking carriage). Common catenary (excluding approximation). Virtual work. Kinematics of uniplanar motion. Rectilinear motion: Simple Harmonic Motion and other laws. Motion in resisting medium.

As to my knowledge, different books will be assigned for both the semester. Ignoring the Physics part, any nice textbook would be of help.

Also, does only Marder contains Jacobian and evelopes? I mean no other books deal with them? Can you suggest me some now?

Thanks verty!

 

[verty]

It would help to know exactly what you know already. Do you know one variable calculus? Do you know integration? Or is this the first course you are doing on calculus? I don't see limits or series in that semester 1, so I think you have done calculus before. How well do you know the one variable stuff?

 

[Saitama]

It would help to know exactly what you know already. Do you know one variable calculus? Do you know integration? Or is this the first course you are doing on calculus? I don't see limits or series in that semester 1, so I think you have done calculus before. How well do you know the one variable stuff?

Yes, I have done calculus before. I very well know one variable stuff and I am good enough at it. I have already done a lot of challenging problems on one variable calculus. I do have some idea about Asymptotes and I have done a few basic exercises on Partial Differentiation and I think I know enough Partial Differentiation to clear my exams. I haven't done Maxima and Minima of two or more variables. I checked it out in the book I am currently assigned and it doesn't seem too difficult. Envelopes, Curvatures and Jacobians are entirely new to me.

About integral calculus, I have done a lot of problems ranging from easiest to the most challenging ones in the past and I still remember a lot of stuff but I never dealt with Beta and Gamma functions, Rectification, Multiple integrals and Differentiation under the integral sign. I have done a few basic problems on Volume and surface of solids of revolution but I will start it from fresh.

Does this help?

PS: You can also have some idea about what I know from the practice sheets I sent you before.

 

[verty]

Here's an option for you, the author is a professor at IIT Delhi so it should be good:

http://justbooks.in/product/textbook-vector-calculus-0

This is assuming you know the one variable material.

 

[verty]

Okay, I just saw your post above, it helps. Why not read chapters 2 and 3 in that Marder book, it'll cover that stuff that you mentioned. I think you are ready for it.

Chapters 4 and 5 are integration but it stops a little early, rectification is just line and surface integrals so it'll cover that as well as multiple integrals, but there is more that it doesn't have. I'll look very quickly for something to cover the rest.

 

[Saitama]

Here's an option for you, the author is a professor at IIT Delhi so it should be good:

http://justbooks.in/product/textbook-vector-calculus-0

This is assuming you know the one variable material.

Does all of the above mentioned topics belong to "Vector Calculus"?

And don't worry that the book I look for should be by an Indian author. I personally prefer book by foreign authors, feel free to suggest any book. I will look if its available in my country. :)

 

[verty]

Does all of the above mentioned topics belong to "Vector Calculus"?

And don't worry that the book I look for should be by an Indian author. I personally prefer book by foreign authors, feel free to suggest any book. I will look if its available in my country. :)

In that case, I'll recommend this book instead:

Mathematical Methods in the Physical Sciences - Boas

It'll cover what is missing and should also help with the ODE semester.

About the other question, yes it is all vector calculus (well, asymptotes and envelopes are geometry) except the Beta and Gamma functions, I'm sure you could read about them online. I don't know what asymptotes is about, so I can't say anything about that.

 

[Saitama]

In that case, I'll recommend this book instead:

Mathematical Methods in the Physical Sciences - Boas

It'll cover what is missing and should also help with the ODE semester.

About the other question, yes it is all vector calculus (well, asymptotes and envelopes are geometry) except the Beta and Gamma functions, I'm sure you could read about them online. I don't know what asymptotes is about, so I can't say anything about that.

That should help, thanks a lot for your time verty!

 

[verty]

Sorry, I forgot about curvature. Have a look here (http://ia801507.us.archive.org//33/items/DifferentialAndIntegralCalculus_109/ ), chapters 5 and 6 for asymptotes and curvature. These geometry topics are not in books I'm familiar with. The other thing is curve tracing which I guess is drawing curves but that should be easy.

That Piskunov book is available but doesn't look too good, I would just look in those chapters.

 

[Saitama]

Sorry, I forgot about curvature. Have a look here (http://ia801507.us.archive.org//33/items/DifferentialAndIntegralCalculus_109/ ), chapters 5 and 6 for asymptotes and curvature. These geometry topics are not in books I'm familiar with. The other thing is curve tracing which I guess is drawing curves but that should be easy.

That Piskunov book is available but doesn't look too good, I would just look in those chapters.

Thank you again verty! :)

Do you have some resources for Polar Coordinates?

 

[verty]

Thank you again verty! :)

Do you have some resources for Polar Coordinates?

Yes, this is easy to answer. Problem set 8A here, do the parametric equations and then the polar coordinate stuff. The lecture notes and part A problems should be enough for you to understand it. There'll be a video too but I don't expect you will need it.

Obviously I would normally recommend a book to learn all this stuff from but in your case, there isn't a lot of time.

 

[Saitama]

Yes, this is easy to answer. Problem set 8A here, do the parametric equations and then the polar coordinate stuff. The lecture notes and part A problems should be enough for you to understand it. There'll be a video too but I don't expect you will need it.

Obviously I would normally recommend a book to learn all this stuff from but in your case, there isn't a lot of time.

Thank you! :)